The expression is simplified -x^4 -3x³ -x² + 4x + 6
What are algebraic expressions?
Algebraic expressions are expressions consisting of variables, constants, factors and coefficients.
They are also made up of arithmetic operations such as addition, subtraction, multiplication, division, etc
Given the expression:
(-x² - 2x - 2) (x² + x - 3)
expand the bracket
-x^4 - x³ + 3x² -2x³ - 2x² +6x - 2x² - 2x + 6
collect like terms
-x^4 - x³ - 2x³ + 3x² - 2x² - 2x² + 6x - 2x + 6
Add or subtract like terms
-x^4 -3x³ -x² + 4x + 6
The expansion of the expression is -x^4 -3x³ -x² + 4x + 6
Hence, the expression is simplified -x^4 -3x³ -x² + 4x + 6
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Write the equation in standard form given the following information (with solutions please)
1. The roots are 1/2 and -1/2
The Quadratic equation in standard form given the following roots are
f(x) = 2x^2 - 3x + 1
The root 1 is associated with the factor (x - 1).
The root 1/2 is associated with the factor (x - 1/2), which in turn is equivalent to (2x -1)
The quadratic in question is f(x) = (x - 1)(2x - 1). To write this in standard form, perform the indicated multiplication:
f(x) = 2x^2 - 2x - x + 1, or f(x) = 2x^2 - 3x + 1
What is Quadratic equation?Any equation in algebra that can be written in standard form as where x is an unknown and a, b, and c denote known numbers, where a 0 is a quadratic equation.
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as a[tex]x^{2}[/tex] + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
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What is 1,837 + 1,283?
Answer:
3,120
Step-by-step explanation:
Does this need an explanation?
Answer:
1,837+1,283= 3,120
Step-by-step explanation:
Hope It Helps
Sorry If I'm Wrong
arc xylocated on circle ahas a length of 40 centimeters. the radius of the circle is 10 centimeters. what is the measure of the corresponding central angle for xy⌢in radians?
We know that an arc is a part of the entire perimeter of a circle.
Radian is defined as a unit of plane angular measurement that is equal to the angle subtended by the circle at the center by an arc that is of the length equal to the radius
We also know that the circle as a whole contains 2π radians
Now first we are required to find the perimeter of the circle
Perimeter of the circle is given by the formula 2πr
Hence, perimeter of the circle = 2πr= 2π x 10 =20π=62.851cm
Hence value of arc in radians = 40/62.851 x 2π =0.636 x 2 π =1.272π
Radian can be converted to degree by multiplying the radian measure by 180/π
Therefore, angle subtended by arc in degrees =1.272 π x 180 /π =229.1 °
Hence the angle subtended by arc is 229.1°
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A recipe had 4 tablespoons of seasoning to 6 cups of flour. So there is _____ of a tablespoon of seasoning for each cup of flour.
Answer:
Step-by-step explanation:
The ratio of seasoning to flour is 4:6.
This can also b re-written as a fraction. The fraction would be 4/6.
If you want to find the amount of seasoning per cup of flour, you must divide.
4/6 Divide the denominator (bottom number) by 6 to get a 1 on the bottom. Now divide the numerator (top number) be the same amount. This gives you a 0.66 on the top. Now you have 0.66/1.
0.66 is equivalent to 2/3, so for every 1 cup of flour, there is 2/3 a tablespoon of seasoning.
Hope this helps!
At most, Alana can spend $40 on carnival tickets. Ride tickets cost $4 each, and food tickets cost $2 each. Alana buys at least 16 tickets. The system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys.
r + f ≥ 16
4r + 2f ≤ 40
A graph shows r on the x-axis, from 0 to 18, and f on the y-axis, from 0 to 20. Two solid lines are shown. The first line has a negative slope and goes through (0, 20) and (10, 0). Everything to the left of the line is shaded. The second line has a negative slope and goes through (0, 16) and (16, 0). Everything above the line is shaded.
What is the maximum number of ride tickets she can buy?
4
6
10
12
The maximum number of ride tickets that she can buy is A. 4.
How to illustrate the information?It should be noted that the system of inequalities represents the number of ride tickets, r, and the number of food tickets, f, she buys.
r + f ≥ 16
4r + 2f ≤ 40
The two inequalities are first shown on the graph as seen in the attachment. The graph demonstrates where the two in-equations intersect (4,12).
Consequently, we can observe that r has a maximum value of 4. This was illustrated in the graph.
In conclusion, the correct option is A.
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an image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor.the actual book is 10.5 inches wide.what scale is being used on the image?
The scale that is being used on the image is 1:7
Calculating scaleFrom the question, we are to determine the scale that is being used on the image.
From the given information,
The image of the book shown on the website is 1.5 inches wide and 3 inches tall
Also, we have that
The actual width of the book is 10.5 inches
The scale = Width of the book on the website / Actual width of the book
Thus,
Scale = 1.5 inches / 10.5 inches
Scale = 1/7
∴ Scale = 1 : 7
Hence, the scale that is being used on the image is 1:7
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The surface area of a cube is 96 cm².
Work out the volume of the cube in cubic centimetres.
The volume of cube in cm is (4cm)
Volume of cube is =96 CM^2
Let's consider he as the edge of cube
Surface area of is =6
That is symbol cube as (e^2)
As per the given question the surface are of cube is given as 96 cm^2
As we know
96=6^2
e^2=96/6
e^=16
e=√16
e=4cm
The volume of cube in centimetre is 4cm
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if the least common multiple of $a$ and $b$ is $1575$, and the ratio of $a$ to $b$ is $3:7$, then what is their greatest common divisor?
The greatest common divisor of two given numbers is 15.
Given that, the least common multiple of A and B is 1575 and A: B=3: 7.
We need to find what is their greatest common divisor.
What is the least common multiple?The least common multiple is also known as LCM (or) the lowest common multiple in math. The least common multiple of two or more numbers is the smallest number among all common multiples of the given numbers.
We know that the product of the GCF and the LCM of two numbers is always the product of the two numbers.
Let the GCF of two numbers be x.
Then A×B=1575×x
Take A:B=3k:7k
Now, 3k×7k=1575×x
⇒21k²=1575x
⇒k²=75x
x must be expressed as a square divided by 75.
Now, 75=3×5×5
If we multiply 3 to the above product we get the perfect square number.
So, k²=225
⇒k=15
Now, 3k=45 and 7k=105
45=3×3×5 and 105=3×5×7
So, GCD=3×5=15
Therefore, the greatest common divisor of two given numbers is 15.
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Your question is incomplete, probably the complete question/missing part is:
If the least common multiple of A and B is 1575, and the ratio A of B to 3 is 7 , then what is their greatest common divisor?
Answer: 75
Step-by-step explanation:
Since the ratio of A to B is 3:7:
There is an integer k for which A=3k and B=7k.
Moveover, k is the greatest common divisor of A and B, since 3 and 7 are relatively prime.
Recalling the identity lcm(A,B)*gcd(A,B)=AB, we find that 1575k=(3k)(7k), which implies k=1575/21=75.
What is the image of the point (-1, -4) after a rotation of 90° counterclockwise
about the origin?
Answer:
(4, -1)
Step-by-step explanation:
See attached image.
At the beginning of the day, the stock market goes down 70 1/2 points and stays at this level for most of the day. At the end of the day the stock market goes up 80 3/4 points from the low at the beginning of the day. What is the total change in the stock market from the beginning of the day to the end of the day?
The change for the day is 10 1/4
In this problem, we are expected to calculate the change in the price of a particular stock
Given that the days high is 80 3/4
and also that the days low is 70 1/2
we can calculate the change by subtracting the days low from the days high
i.e 80 3/4- 70 1/2= 323/4-141/2= (323-282)/4= 41/4
hence the change for the day is 41/4 =10 1/4
Also we can calculate the percentage change as
%change = (high-low)/low*100
%change= 80 3/4- 70 1/2/70 1/2*100= 41/4/70 1/2 *100
%change= 41/4*2/141*100
%change= 0.00145=0.145%
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Select the correct answer. Triangle is reflected across the y-axis and then dilated by a factor of centered at the origin. Which statement correctly describes the resulting image, triangle ? Image of right triangle ABC in a graph with vertices A (minus 4, minus 2), B (4, minus 2), and C (4, 4) A. Both the reflection and dilation preserve the side lengths and angles of triangle . B. Neither the reflection nor the dilation preserves the side lengths and angles of triangle . C. The dilation preserves the side lengths and angles of triangle . The reflection does not preserve side lengths and angles. D. The reflection preserves the side lengths and angles of triangle . The dilation preserves angles but not side lengths.
Answer: B (4 minus 2)
A set contains 23 elements set B contains 15 elements, and 13 elements are common to sets A and B how many elements are in set A
A contains 21 elements
Let's assume set A contains X elements ,
so , according to set theory , A ∪ B = 23
or, A + B - ( A ∩ B ) = 23
or ,X + 15 - 13 = 23
or, X + 2 = 23
or , X = 23 - 2
or, X = 21
So , there are 21 elements are present in set A .
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Solving the problem according to the set theory, we get that set A contains 21 elements.
A set is a well-defined collection of objects, whose elements remain fixed and do not vary. It means that set doesn't change from person to person and is invariable.
Let's assume that set A contains X elements,
So, according to the set theory, A ∪ B = 23
or, A + B - ( A ∩ B ) = 23
or ,X + 15 - 13 = 23
or, X + 2 = 23
or , X = 23 - 2
or, X = 21
From the above explanation, we get that there are 21 elements are present in set A .
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what type of measurement scale is used for operating system? nominal scale ordinal scale interval scale ratio scale
We can actually deduce here that the type of measurement scale that is used for operating system is: Nominal scale.
What is nominal scale?A nominal scale is actually known to be a measurement scale whereby numbers are used as “tags” or “labels” only in order to identify, locate or classify an object.
This measurement scale actually deals only with non-numeric variables. It can be used where numbers have no value.
Other measurement scales include:
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can u explain why please, i need a explanation.
PLEASE SHOW WORK
----------------------------------------
Answer:
Perimeter = 2(length) + 2(width)
Perimeter = 2(17.4x - 0.8) + 2(6X)
Perimeter = 34.8x - 1.6 + 12x
Perimeter = 46.8x - 1.6
0.6244 in scientific notation
Answer:
6.244 x 10^-1
Step-by-step explanation:
money marilyn is going on a class outing to an amusement park. she has $40 to spend. the admission price is $20. she plans to buy a sandwich for $5. a cup of lemonade costs $3.00. write an inequality to show how many cups of lemonade, c, she can buy.
Money Marilyn can buy 1≤ x≤5 (more than or equal to one and less than or equal to five) cups of lemonade from the rest of the money.
Here we have,
Total money to spend= $40
Admission price= $20
Sandwich= $5
Add all expenses to find the money spent by Money Marilyn.
Total expense= admission price + sandwich
Total expense = $20 + $5 = $25
Amount left with her= $40-$25 = $15
The number of cups when each cup's cost is $3
Total lemonade(x) = $15/$3 = $5
In an equality,
Money Marilyn can buy 1≤ x≤5 (more than or equal to one and less than or equal to five) lemonades from the rest of the money.
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assuming that the value of x is 4, and the value of y is 6, what is the value of the following expression? (x - y)**2 > y
The result of the expression "(x - y)**2 > y" is -4>6 and it is false.
Information about the problem:
(x - y)**2 > yx = 4y = 6To solve this problem, we have to substitute the values of (x) and (y) and solve the equation:
(x - y)**2 > y
(4 - 6)**2 > 6
-2 ** 2 > 6
-4 > 6
The expression is false because - 4 is not higher than 6. The correct expression is:
(x - y)**2 < y
-4 < 6
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
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PLS HELP
ANSWER QUESTION QUICK
PLEASE SHOW WORK
Given the function g(x) = x² − 3, find the value of g (−2).
how do i multiply fractions?
Answer:
The first step when multiplying fractions is to multiply the two numerator. The second step is to multiply the two denominators. finally, simplify the new fractions. The fractions can also be simplified before multiply by factoring out common factors in the numerator and denominator.
example equation: 3/4 x 2/5
1) line equation
3 2
_x_
4 5
2) nominators x nominators, denominators x denominators
3 2 6
_x_=_
4 5 20
4) simplify
6/20=3/10
good luck !!
Which number is Irrational?
a
square root 9
b
0.123123123....
c
5/9
d
0.2535455565....
Answer:
Step-by-step explanation:
d. Square root of 9
you’re welcome :)
The irrational number is 0.2535455565.....
The correct option is D.
Given, that identify the irrational number.
Irrational number : Irrational numbers are non terminating and non repeating.
1) Square root of 9: √9
= 3
It is rational number.
2) Number : 0.123123123....
It is Non terminating but repeating thus it is not an irrational number.
3) Fraction : 5/9
5/9 = 0.555555..
It is a repeating number thus its is not an irrational number.
4) Number: 0.2535455565....
The number is non terminating as well as non repeating. Thus it is an irrational number.
Therefore option D is correct.
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help me please i do not understand this assignment
Answer: 164.53%
Step-by-step explanation:
105.3/64=1.6453125
1.6453125*100=164.53125
164.53125=164.53%
Notice the answer is greater than 100 percent. This is because 105.3 is greater than 64, meaning that 105.3 is greater than 100% of 64, so 105.3 will have a greater percent value.
2. If freezing rain is falling, then the air temperature is 32°F or less.
Converse:
Inverse:
Contrapositive:
Answer:
Converse: If the air temperature is 32°F or less, then freezing rain is falling.
Inverse: If freezing rain is not falling, then the air temperature is not 32°F or less.
Contrapositive: If the air temperature is not 32°F or less, then freezing rain is not falling.
Explanation:
Statement: If p, then q.
Converse: If q, then p.
Inverse: If not p, then not q.
Contrapositive: If not q, then not p.
A bag of oranges costs 6.40 dollars there are 16 oranges in each bag what would be the cost of 48
Answer:
Step-by-step explanation:
bag of oranges = $6.40
each bag = 16 oranges
48 divided by 16 = 3 (bags)
$6.40 x 3= $19.20
The cost of 48 oranges would be $19.20 when the each cost 6.4
Given:
- Cost of a bag of oranges = $6.40
- Number of oranges in each bag = 16
First, let's find the cost per orange:
Cost per orange = Cost of a bag / Number of oranges in the bag
Cost per orange = $6.40 / 16 = $0.40
Now, the cost per orange is $0.40.
To find the cost of 48 oranges, multiply the cost per orange by the number of oranges:
Cost of 48 oranges = $0.40 * 48 = $19.20
Therefore, the cost of 48 oranges would be $19.20.
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What are the sides of ∠JBA ?
The sides of angle JBA is ray BJ and BA.
What is an angle ?In the geometry, angle is defined as the geometry formed by the multiple rays. Or we can say that the angle is the figure formed by two rays which has same initial point. These rays are also known as the sides of an angle. A angle can have two rays.
Some common terms related to angle :
Endpoint : It is the point where the rays met to each other.
Ray : Ray is the side or line segment on which angle is formed.
Curve : It is a line but not straight i.e. a bended line.
Tangent : A line which touches the surface of curve.
In the given question, as ∠JBA is made between two lines or rays i.e. ray BJ and ray BA . Therefore sides of this angle are BJ and BA.
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Which expression is equivalent to 1/3 (2x + 12) - 14/15
A: 1 3/5x + 4
B: 4/15x - 4
C: -4/15x - 4
D: -4/15x + 4
Answer:
D.
Step-by-step explanation:
First distribute:
2/3x + 4 -14/15x
2/3 = 10/15
10/15-14/15=
-4/15
-4/15 + 4
the greatest of the 21 positive integers in a certain list is 16. the median of the 21 integers is 10. what is the least possible average (arithmetic mean) of the 21 integers?
The least possible average (arithmetic mean) of the 21 integers is 6.
Let the list be arranged in ascending order.The median of the list, i.e., the 11th term in the list, is 10.The greatest number in the list, i.e., the 21st term, is 16.We need to minimize the mean, so we will choose the smallest numbers.For the first 10 elements, we can choose the smallest positive integer, i.e., 1.The first 10 terms are all equal to 1.We must choose numbers greater than or equal to 10 for elements 12 to 20. We will choose 10 in order to keep the average at its minimum.The terms from the 11th to the 20th position are equal to 10.The 21st term is 16.The sum of all the terms is (1*10) + (10*10) + 16.The sum of all the terms is 10 + 100 + 16.The sum of all the terms is 126.The mean is calculated as the sum of all terms divided by the total number of terms.The mean is 126/21.The mean is 6.To learn more about the arithmetic mean, visit :
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Which of the following is the solution to 3 | x-1 | > 12?
A. x≤-3 or x >5
B. x > -3 or x > 5
C. x < -3 and x > 5
D. X > 5
Answer:
7
Step-by-step explanation:
8-9-6
Paul runs a small farm. After the last harvest, he weighed the amount of squash he collected. He had 42.2 total pounds of green and yellow squash. If yellow squash made up 1 5 of the harvest by weight, how many pounds of green squash did he have? Write your answer as a whole number, decimal, fraction, or mixed number. Simplify any fractions.
The weight of the green squash is 33.76 pounds.
What is the weight of the green quash?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/4. A decimal is a non-integer that is made up of integers and non-integers that are separated by a decimal point. An example of a decimal is 1.2.
The weight of the green squash can be determined by multiplying the fraction of the green quash by the total pounds of green and yellow squash.
Pounds of green squash = fraction of green squash x total pounds of squash
Fraction of green squash = 1 - 1/5 = 4/5
Pounds of green squash = 4/5 X 42.2 = 33.76 pounds
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